Msc Project report DSP based Adaptive Filter
Contents
1. Z Grid and Cross MEI Ix 13 cee Se e Colour Line Width Enable Background R Graph L DSP based Adaptive Filter Figure 5 7 Settings a Form for sttings b Form for color settings The command button Settings is used to perform settings to the apperance of the graph User can set whether they want the learning curve to be plotted in a graph with grid or without grid b clicking User can even choose color for the graph background grid and etc The window for the setting form is shown in Figure 5 7 a When user click on the color settings the form shown in Figure 5 7 b will be displayed Chapter 6 34 DSP based Adaptive Filter Conclusions The literature survey and research carried out in this project primarily focuses on understanding the fundamentals and characteristics of the adaptive algorithm By having this information it is then being implemented as a software tools to enable user to determine the characteristic and performance of adaptive filter algorithm This chapter summarizes the research work that had been carried out in this project Besides that it also include the summaries the project report specifying the aims and objectives achieved in this project research and some pointers to future development of this project work 6 1 Project Achievements The main purpose of this project is to study the fundamental concept of adaptive filtering and then implem2. gt axix n E ja Kiaat 2 4 k 0 The structure releasing this equation is called the direct form and is shown in Figure 2 4 DSP based Adaptive Filter ao n x n E d i a n VA bi n i y n 7 7 x n 1 Y Vi be at y n 1 z a n ban z x n 2 2 Da y n 2 v ax n by 1 n v 7 7 x n N 1 y n M 1 Figure 2 4 Direct form of IIR filter The coefficient a and b are the feed forward and feedback tap weight respectively From equation 2 4 it can be observed that the value of the present filter output sample y n is a function of past outputs y n k as avell aS present and past input samples x n k This structure forms a pole zero filter design where coefficients a control the zero location and coefficients b control the pole location 3 The advantage of IIR filter is that it is possible to realize sharp cutoff filter characteristic with the inclusion of poles and zeros But one major problem with adaptive IIR filter design is the possible instability of the filter since poles could be outside the stable region 5 22 3 Comparison of Finite Impulse Response Filter and Infinite Impulse Response Filter In adaptive filter applications Finite Impulse Response FIR filter is more commonly used compare to Infinite Impulse Response IIR filter This is mainly because the design structure and the characteristics of FI
3. It is used to measure how well does the system resisting noises For LMS no matter what the initial condition for the weights the solution always converges to basically the same value This robustness is rather important for real world problems where noise is universal Robustness of a system can also be affected by the choice of LMS algorithm parameter 4 2 Simulation and Result In this section two experiments had been carried out in order to see how do the step size and the filter s length affect the performance of LMS algorithm The simulation and the result are displayed as leaming curve of MSE and tap weight The simulation will clarify the properties of L MS algorithm which has been discussed in section 4 1 4 2 1 Experiment 1 The first experiment is to observe how the step size u affect the convergence rate So a set of parameter is used to perform this experiment Here the LMS algorithm parameter is set to be 21 DSP based Adaptive Filter e I oc C a 28 Z Da Se E E 25 28 4 D S o0 mH 8 zZ 180 1160 140 c Using the above parameter and applied to the software the results of varying the step size are obtained This software provides learning curves of the system where Square Error performance of the system while Figure 4 3 shows performance of the performance of the system can be analyse from this curves Figu
4. b will pop up user just need to select which text file that contain information of tap weight After selecting the text file the value of tap weight will be assigned to correspond list box The whole process can be summarized as follow Click Open File or press Alt O Click on the destination that the imported data will be located Select the path which data is imported from Finally the imported data will be assigned to the correspond location 31 DSP based Adaptive Filter HE w Formi File Open File Tap wei Tap Input Desired Reponse File name a Open File is selected Files of type Text Files TXT ai Cancel Open as read only b Dialog Box Figure 5 4 5 2 3 Clear For user to clear all the parameter user can press Alt F and then click on Clear as shown in Figure 5 2 a Basically the method used here is the same as loading example which has been discussed in section 5 2 The whole process of clearing all the value in their corresponding location can then be summarized as follow Click on File or press Alt t F Click on Clear 5 2 4 Displaying Learning Curve After assigning all the parameters user can click Enter in order to view the learning curve of the adaptation process This curve as had been discussed in chapter 4 can be used to determine how well is the adaptation convergence rate stability etc The lerning curves for MSE performance
5. 1 Project Achievements 6 2 Future Works 7 Appendix A Program Code of Adaptive Filter Implementation 8 References List of Figure Figure 2 1 Figure 2 2 Figure 2 3 Figure 2 4 Figure 2 5 Figure 2 6 Figure 2 7 Figure 2 8 Figure 3 1 Figure 3 2 Figure 3 3 Figure 3 4 Figure 4 1 Figur 4 2 Figure 4 3 Figure 4 4 Figure 5 1 Figure 5 2 Figure 5 3 Figure 5 4 Figure 5 5 Figure 5 6 Figure 5 7 Block diagram of adaptive filter Transversal FIR filter Adaptive transversal filter Direct form of IIR filter Adaptive System Identification Configuration Adaptive Inverse System Configuration Adaptive Noise Cancellation Configuration Adaptive Linear Prediction Configuration Visual Basic s design environment Flowchart for the LMS adaptive filter a Discrete signal of input data b Discrete signal of input signal after one delay The convolution y n of x n and w n MSE performance using step size of a 0 5 b 0 1 and c 0 05 OND Ww BR 10 10 11 13 14 15 16 22 Tap weight performance using step size of a 0 5 b 0 1 c 0 0523 MSE performance using filter length of a 2 b 8 and c 10 Tap weight performance using filter length of a 2 b 8 c 10 Adaptive based Software GUI Flowchart of Software Software GUI when certain events are clicked a File b Load Example a Open File is selected b Dialog Box Window displaying Learning Curve Dialog Box for saving graph Se
6. List n arr n List1 List n List1 List n arr n Next Next If Option4 Value True Then form graph list x Additem z form graph list y AddItem List1 List Q form graph gph data form graph gph data 1 form graph label x Caption No of Iteration n form graph label title x Caption No of Iteration n End If z z 1 Loop load graph form graph Visible True If Option1 Value True And Option3 Value True Then form graph label title y Caption Mean Square Error MSE form graph label y Caption Mean Square Error MSE form_graph gph log False fortm graph func gph setting form graph func gph plot form graph Caption Learning Curve Elself Option2 Value True And Option3 Value True Then form graph label title y Caption Mean Square Error MSE log form graph label y Caption Mean Square Error MSE log form graph gph log True form graph func gph setting form graph func gph plot form graph Caption Learning Curve Elself Option4 Value True Then form graph label title y Caption Tap Weight form graph label y Caption Tap Weight form graph gph log False form graph func gph setting form graph func gph plot form graph Caption Learning Curve End If End Sub Private Sub Command2 Click End End Sub Private Sub Desired Click Dim temp As String CommonDialogl Filter Text Files TXT TXTJAII Files CommonDialog1 ShowOpen RichTextBoxl LoadFile Commo
7. adjustment These filters can change in accordance to their input signals An adaptive filter is used in applications that require differing filter characteristics in response to variable signal conditions An adaptive filter has the ability to update its coefficients New coefficients are sent to the filter from adaptive algorithm that modifies the coefficients in response to an incoming signal The digital filter is typically a special type of finite impulse response FIR filter but it can be also an infinite impulse response IIR or other type of filter 2 1 Structure of Adaptive Filter Adaptive filter consists of two parts which are a programmable digital filter and an adaptive algorithm The programmable digital filter is designed to produce a desired output with respect to a sequence of input data Where else the adaptive algorithm is used to perform adjustment to the tap weights of the filter Figure 2 1 shows the structure of an adaptive filter d n A Programmable x n TS 2 Digital Filter yn lt das Adaptive PI Algorithm Figure 2 1 Block diagram of adaptive filter This filter has a reference input signal x n an output signal produced by the programmable digital filter y n a desired response d n and error e n which is the difference between desired response and output signal The adaptive algorithm then adjusts the tap weights of the digital filter in order to minimize the me
8. can be plotted either in ratio or logarithm form User can select wheteher they want to view MSE performance or tap weight performace of LMS algorithm by selecting the option button on the right hand site of the software refer to Figure 5 1 From this graph user can click on the command buttons which are located at the right hand side of the graph as shown in Figure 5 5 These buttons will act differently if user clicks on them For the button named Close it will close the entire window form in Figure 5 4 While the button named Refresh is to refresh the graph 32 DSP based Adaptive Filter Learning Curve Command Buttons 84 593841552734 Mean Square 322535541 65091 Error MSE loa Mean Square Close Error MSE loq Refresh Save As I 1 1 ie 1 1 1 r 1 1 b 1 1 1 r 1 1 L 1 1 1 r ico io 120 140 1160 Setting No of Iteration n Figure 5 5 Window displaying Learning Curve When user click on the button named Saved As then dialog box shown in Figure 5 6 will pop Here user can save the graph as bitmap bmp file for reference purposes Save in 3 My Documents gt m al ei Final Project My Pictures Game Ga My Webs Messenger Service Received Files send MusicDownload an graph Fi igure 5 6 Dialog Box My eBooks sn Mu 020 gu 8 My Music for saving graph ume E Save as type JBitmapt bmo Cancel Open as read only
9. convergence rate 20 DSP based Adaptive Filter 4 1 4 Stability Stability of an adaptive system is a very important to determine the performance of an adaptive system In real world it is difficult to obtain a completely stable adaptive system but a reliable system can be obtained when certain LMS algorithm parameter is adjusted For instance the step size u can affect the stability of the system With large step size u it obtains faster convergence time but the stability of the system will decrease Conversely when smaller step size u is used the stability of the system will increased One aspect that have to be take into account is that larger step size u improved the convergent rate hence lead to simpler computational complexity Thus system has to be designed with respect to all this aspect 4 1 5 Computational Complexity Computational complexity is another aspect to be considered when an adaptive system is being modelled In real time when a system is being implemented hardware limitations can bring a huge problem to the performance of a system When a system is designed using a much complex algorithm it requires much greater hardware resources than a simpler algorithm This is the reason LMS algorithm is much more preferred compared to RLS algorithm 4 1 6 Robustness One of the interesting aspects of the CMS solution is its robustness Robustness of a system is directly proportional to the stability of a system
10. n w n 1 ke n 2 7 where k is the Kalman gain and e n 1s the error signal Basically RLS algorithm implemented in transversal FIR filter is similar to the LMS algorithm in the term of obtaining the digital filter yn The only different is in the adaptation process where RLS uses least square method Here the Kalman gain vector is based on input data auto correlation results the input data and a factor called the forgetting factor The forgetting factor can be in the range between zero and one The 2 4 Adaptive Filtering Application The uniqueness of adaptive filter where it can operate in an unknown environment makes it so powerful and suitable to be applied into a lot of Digital Signal Processing DSP fields such as communications radar sonar etc 1 For adaptive filter there are at least four system configurations that can be set up which are Adaptive Identification System Adaptive Inverse System Adaptive Linear Prediction and Adaptive Noise Cancellation 2 4 1 Adaptive Identification System Configuration Adaptive Identification System Configuration can be applied as Modem Echo Cancellation Layered Earth Modelling etc The architecture of this system configuration is illustrated in Figure 2 5 Unknown lt System d n o Dr Adaptive x n Filter y n Figure 2 5 Adaptive System Identification Configurations DSP based Adaptive Filter As shown in Figu
11. predict the future element of the input signal x n based on previous observation 11 DSP based Adaptive Filter Chapter 3 Implementation of Adaptive Filter Algorithms using Visual Basic In previous chapter the structures and various configurations of adaptive filters had been discussed Now in this chapter the adaptive filter algorithms will be discussed in more detail where it is the main purpose of the project As had been discussed in Chapter 2 basically there are two common adaptive filter algorithms the Least Mean Square LMS and the Recursive Least Square RLS algorithms Here the main focus will be the Least Mean Square LMS algorithm Thus it is wise to understand how does this algorithm actually being designed and work using Visual Basic Language 3 1 Introduction of Visual Basic Visual Basic language is a programming language which works well with the Windows operating system Thus it can be said that this language is used to create Windows based applications This language is very popular with the ability of creating graphical user interface GUI program Typical drag and drop techniques are used to design the software A Visual Basic application is make up by small components The most common components are form control and procedures Forms are the windows upon which used to build user interface Controls are interface tools such as label text boxes and command button where each of it have their own func
12. system is said to be accurately modelled has small value of minimum MSE where else a large minimum MSE that the system is not accurately modelled 4 1 3 Filter Length The filter length indicates the accuracy of a system which can be modelled by the adaptive system It affects the convergence rate the stability of the system and the minimum mean square error Misadjustment M is defined as the ratio of the steady state value of the excess mean square error to the minimum mean square error It is used to measure how close the LMS algorithm is to optimality in the mean square error sense Therefore the adaptive filtering system is accurately designed if the misadjustment M is small The computation time of LMS algorithm is inversely proportional to the misadjustment M The filter length will affect the convergence rate by varying the computation time When the filter length of a system is increased automatically the computation time will increase Hence as filter length increased the misadjusment will decrease and this lead to faster convergence rate For stability an increase in filter length may add additional poles or zeros that may be smaller than those that already exist So in order to maintain stability the maximum convergence rate has to be decreased When a system has too many poles and zeros for system modelling it will have potential to converge to zero However this will increase the calculation which will then affect the maximum
13. txt files Computation to the software of filter Enter adaptive Select graph algorithm specification parameter Figure 5 2 Flowchart of Software Figure 5 2 illustrate the flow of software in a flowchart manner Basically this is how the software being program to run Stage 1 Assign signals parameter in txt files This stage user have to put all the information of the signal s in txt files For instance tap weight user have to assign each tap weight in vertical manner in txt files because the program will read the data from txt files in vertical manner Stage 2 Load txt files to the software From txt files user can load the information of the respective signals to the corresponding destination After the information of the signal is loaded into the program then this is the value where the program will use to perform simulation Stage 3 Enter adaptive algorithm parameter User then have to set the parameter of the adaptive algorithm the step size filter length etc 29 DSP based Adaptive Filter Stage 4 Select graph specification User have to select which graph specification he want to view in order to investigate the performance of the adaptive filter For instance choose between Mean Square Error in ratio form or in logarithm form Stage 5 Computation of filter After all parameters of the adaptive system is being defined then by clicking Enter refer to 5 2 4 the prog
14. 140 160 By 1100 120 1140 1160 1180 1100 120 1140 1160 1180 Figure 4 3 MSE performance using filter length of a 2 b 8 and c 10 25 DSP based Adaptive Filter No Filter Length N Tap weight No ofiteration a 2 0 7763 185 8 0 7929 150 C 10 0 7930 120 Table 4 2 Results obtained when using different filter length for tap weight analysis The graph parameter of Figure 4 4 y axes Tap Weight x axes No of iteration n chia caver evita pe aoe a A M ocn Pa E ha SJ SUI RR maale eae ses i 4 1 1 1 1 1 i i i i i A a A A i i D e seq emm mum me i D 1 ae ee see eee ty 1 I 1 1 1 D D TR 4 B 4 i i i i i D i mna p 4 p j bR j R j i D R 4 2 2 2 R 4 i D 120 1140 1160 1180 Figure 4 4 Tap weight performance using filter length of a 2 b 8 c 10 As for the performance of tap weight a system with a larger filter length will adapt to the optimum weight in lesser convergent time Besides that it also converges to the optimum 26 DSP based Adaptive Filter weight where it is quite near to the optimum value One can refer to Figure 4 4 to have a better description of how the filter length affects the performance of the LMS a
15. 2 Adaptive Filter 2 1 Structure of Adaptive Filter 2 2 Programmable Digital Filter 2 2 1 Finite Impulse Response FIR filter 2 2 2 Infinite Impulse Response IIR filter 2 2 3 Comparison of Finite Impulse Response Filter with Infinite Impulse Response Filter 2 3 Adaptive Algorithm 2 3 1 Least Mean Square LMS adaptive algorithm 2 3 2 Recursive Least Square RLS adaptive algorithm 2 4 Adaptive Filtering Application 2 4 1 Adaptive Identification System Configuration 2 4 2 Adaptive Inverse System Configuration 2 4 3 Adaptive Noise Cancellation Configuration 2 4 4 Adaptive Linear Prediction Configuration Implementation of Adaptive Filter Algorithm Using Visual Basic 3 1 Introduction of Visual Basic 3 2 Designing Adaptive Filter Algorithm 32 1 Implementation of Least Mean Square Algorithm 3 2 1 Implementation of Recursive Least Square Algorithm Property and Performance of LMS Algorithm 4 1 Properties of LMS Algorithm 4 1 1 Convergence Rate 4 1 2 Filter Length 4 1 4 Stability 4 1 5 Computational Complexity 4 1 6 Robustness 4 2 Simulation and Result 4 2 1 Experiment 1 4 2 2 Experiment 2 4 3 Summary Software Description 5 1 Software Overview 5 1 2 Flow of Software 5 2 User s Manual ADNAN kx VI VI DOL E NO NO OOO 10 11 12 12 13 13 17 19 19 19 20 21 21 21 21 22 24 27 28 28 29 30 5 2 1 Load Example 5 2 2 Assigning Signal Parameter 5 2 3 Clear 5 24 Displaying Learning Curve 6 Conclusion 6
16. Ko D E NO OON e i D MES E ON D i 1 a ee u A RN ue Nu pre ss Step size 0 5 0 1 0 05 No DSP based Adaptive Filter Table 4 1 Results obtained when using different step size fortap weight analysis The graph parameter of Figure 4 2 y axes Tap Weight x axes No of iteration n Figure 4 2 Tap weight performance using step size of a 0 5 b 0 1 c 0 05 As can be observed in the simulation shown in Figure 4 1 the step size of 0 5 can obtain the fastest convergence rate compare to the others Hence this prove that step size do affect the convergence rate As has been discussed in section 4 1 the step size should DSP based Adaptive Filter meet the condition in equation 4 1 in order to successfully converge to the optimum weight One should remember all the graphs shown in Figure 4 1 are learning curve of measuring Mean Square Error MSE So from the beginning the Mean Square Error MSE is large As more iteration goes on the MSE started to drop and then converge to constant state This curves proved that the MSE do decay exponentially as more iterations is perform Figure 4 2 shows the learning curve of tap weight performance As the initial tap weight of all filters are set to zero thus the tap weight ofthe filter will approach optimum weight as iteration increased Note that the step size of 0 5 is the fastest The optimum weight for this ex
17. Msc Project report Msc in Electrical and Electronics Engineering Communication System DSP based Adaptive Filter Yoke Yen FOO August 2002 DSP based Adaptive Filter by Yoke Yen Foo Report submitted to the Department of Electronics Communications and Electrical Engineering of the University of Hertfordshire in partial fulfilment of the requirements for the award of Master of Science Supervisor Prof Talib Alukaidey Abstract Rapid Digital Signal Processing DSP development has contributed to lots of invention in today s technology DSP are mainly with the digital representation of analogue signals which is continuous with time signal that had been sampled at regular intervals and then converted into digital form When a signal is corrupted by noise filters are used to extract the signals from noise in order to obtain the noise free source There are basically two ways of designing a filter where one is by knowing the exact information of the signal source property the conventional filter and the other one is the contradiction of the previous statement where no exact information of the signal source property is known This type of filter is named adaptive filter Adaptive filter consists of two distinct parts which are digital filter and adaptive algorithm Adaptive filter is used to perform a desire processing and to adjust the coefficient ofthe filter respectively In this report it is mainly discussing the adaptive
18. R filter Finite Impulse Response FIR filter has a finite memory and have excellent linear phase characteristics There is no phase distortion being introduced into the signal by the FIR filter where else Infinite Impulse Response IIR filter produce non linear phase distortion 2 Hence FIR filter is more reliable to be implement compare to IIR filter DSP based Adaptive Filter FIR filter design is always stable since it only involves zeros and reliazed non recursively but IIR filter is not always stable due to its design involves both zeros and poles IIR filter requires fewer coefficients which then contribute to sharp cutoff but the drawback is that it will become unstable When fewer coefficients are required in filter design it means processing time and storage will decrease 2 3 Adaptive Algorithm The most important part of an adaptive filter is the adaptive algorithms It has very unique features where it will vary the tap weights filter in order to minimize the mean square error MSE according to some criterion The most common adaptive algorithm for adaptive filter application is the Least Mean Square LMS and Recursive Least Square RLS Both of these algorithms have their own advantages over each other where it depends on the application 2 3 1 Least Mean Square LMS Adaptive Algorithm Widrow and his coworkers develop LMS algorithm in 1975 This algorithm is widely used in adaptive signal processing such as noise ca
19. algorithm how does it function The adaptive filter using Least Mean Square LMS adaptive algorithm and FIR digital filter is the main concentration Then this structure is modeled as software using Visual Basic language Thus from literature search of adaptive filter it will then describing the technique of converting concept into a software tool The performance of LMS algorithm is then being carried out and is analyze Acknowledgments I would like to take this opportunity to express my gratitude to my project supervisor Prof Talib Alukaidey for all the help he had supplied throughout the entire process of developing this project He has been a very supportive supervisor and under his supervision I managed to learn a lot in various aspects Besides that I would also like to thank Mr Loo Kok Keong who is currently doing PhD programme in Engineering department His advice and useful criticism help to boost my enthusiasm towards this project I would also like to thank my entire friend for being there for me when I need their support They are so helpful that I didn t imagine there could be such a great friend and helper Finally I would like to thank my family for their love and support There are being so great to me especially when I am in pressured Yoke Yen Foo August 2002 Contents 1 Introduction 1 1 General Description of Adaptive Filters 1 2 Project Aims and Objectives 1 3 Project Outline 1 4 Report Outline
20. also lead to other disadvantaged t the system such as stablity will be affected Eventhough RLS algoritm is not succesfully being implemented into the software but the concept of RLS has been studied There are a lot of reason which lead to the failure of implementing RLS algorithm into the software One of the main reason is because RLS algorithm is much more complex than LMS algorithm Besides that time comsumption for this project also contribute to 35 DSP based Adaptive Filter the failure Other than that Visual Basic language sometimes cannot suppott a large computational This is the draw back of using this programming language eventhough it has a very interesting user interface environment Basically this project is a very interesting project and can be used as a learning tool for student to get familiar with adaptive filter algorithm 6 2 Future Works The choice of adaptive algorithm of adaptive filtering system is very important For adaptive filtering system there are several adaptive algorithm such as Least Mean Square LMS Recursive Least Square RLS Normalized LMS NLMS etc As in this software only LMS algorithm is successfully implemented Thus one can upgrade this software into more efficient software by providing various choice of adaptive filtering algorithms Besides that this software can also be implementd into different adaptive filtering configurations In real world the structure of all this confi
21. an square error Thus from sample to sample the tap weights of the digital filter will be updated DSP based Adaptive Filter 2 2 Programmable Digital Filter There are two types of linear digital filter finite impulse response FIR and infinite impulse response IIR filter which can be used to implement adaptive filters 2 2 1 Finite Impulse Response FIR Filter There is basically several FIR realization structures such as transversal structure linear phase structure frequency sampling structures and etc The transversal structure is the most simple structure compare to others It s simplicity is th main attraction of this structure where it is easy to program and efficient 1 2 The transversal filter structure or is more known as tapped delay is the most popular FIR structure and is depicted in Figure 22 x n 1 x n 2 x n N 1 MN De A UE LG Nx s S E ka 20 1 gt gt y n Figure 2 2 Transyersal FIR filter x n Basically it consists of three elements which are unit delay element multiplier and adder 1 In Figure 2 2 the symbol Z represents a delay of one sample where x n 1 is x n delayed by one sample The number of delay element shown as N 1 or known as filter order is use to determine the finite duration of the impulse response 1 The multiplier in the filter is used to multiply the tap input with the respective tap weight filter co
22. ce Hall Inc Englewood Cliffs NJ 1990 41 42
23. e number of iterations approaches infinity Second the average mean square error approaches a constant value as n oo Both of these requirements can be satisfies if a proper step size is used which it has the following condition 0 SHK 2 4 1 total input power where the total input power is the sum of the mean square values of the tap inputs u n u n l u n N 1 Hence this show that the step size play an important role in LMS algorithm that affects the convergence rate of this algorithm A proper step size is needed to avoid misadjustment of Mean Square Error MSE 19 DSP based Adaptive Filter 4 1 2 Mean Square Error MSE Mean Square Error MSE is the parameter which used to analyse how wellis the adaptive system being accurately modelled It is the metric of measuring the performance of the adaptation for the filter s weight to converge to the solution for the system Normally the final value of mean square error J n produced by the LMS algorithm is constant at the end of the convergence The mean square error J n can be obtained by J n e n 4 2 Thus if this is satisfied this algorithm is said to be convergent in the mean square The curve obtained by plotting the mean square error with respect of the number of iteration n is known as learning curve The learning curve of LMS algorithm consists of a sum of errors each of which corresponds to the number of tap weights An adaptive
24. e programming e Toundetstand more precisely about theory and application of FIR adaptive filter for different system configurations e To develop good skills of managing project by providing a good time management DSP based Adaptive Filter 1 3 Project Outline This project is mainly about designing software tool to enable engineers and designer to choose the best adaptive algorithm for FIR adaptive filter in order to get the best performance out from the system configurations So before they choose which adaptive algorithm to use instead of using the old way performing calculation and testing with equipments then monitor result engineer can use this tool to minimize their work In this project Visual Basic Language is used to create the software This language is chosen mainly because it can create programs that work with the Windows operating system It is an event driven language where it responds to events tojexecute different sets of instruction Besides that it is also an object oriented language where it provide graphical user interface GUI 1 4 Report Outline The entire project has been divided into several sections such as section for literature search software design and testing Thus in this report ithas several chapters where each chapter will discussed the research work that has been done in order to develop this project In chapter 1 it is basically an introduction for reader to understand what is this
25. edure is a segment of code that is executed when a particular event occurs to a particular object Thus the event procedure is corresponding to events In this project the main reason of using Visual Basic 6 0 as a development tools is because it has graphical user interface GUI User of this software can easily applying inputs to the program and the result is then displayed either using graphical method or text method 3 2 Designing Adaptive Filter Algorithm Adaptive filter using LMS algorithm is designed based on the mathematical flow of obtaining LMS weight s update equation 3 2 1 Implementation of Least Mean Square Algorithm As mentioned in section 2 3 1 LMS is based on the steepest descent algorithm where the weight is updated from sample to sample in order to minimize the mean square error MSE The computational procedure to design the LMS algorithm using Visual Basic is based on the LMS computation model illustrate in Figure 3 2 13 DSP based Adaptive Filter The whole LMS computation model can be broken down to several stages as shown in Figure 3 2 It is wise to understand how does each block of the flowchart function gt to come out with a process of updating the filter s weight Initialise w n and x n k gt Read d n and x n v Filter x n y n X win x n k Computer error e n d n y n Compute factor e n l Update coefficient w n 1 w n
26. efficient For instance multiplier connected to the n tap input x n k produces product of wy x n k for k 0 1 2 N T From the structure in Figure 2 2 the tap weight vector wi n is represented as w n prot wO n w0 n 2 1 the tap input vector x n s as x n x n x n 1 x n N 1 2 2 The filter output for transversal filter can be expressed as y n w x n k 2 3 DSP based Adaptive Filter x n 7 x n 1 pi 7 x n 2 pi 7 x n N 1 pa vot fn won wmm yp 7 Adaptive 4 e n 4 yn Algorithm C ET Figure 2 3 Adaptive transversal filter Figure 2 3 shows the structure of the transversal filter in the implementation of adaptive filter using FIR digital filter This filter has a single input x n and an output y n The output is generated using equation 2 3 Here there iS a desired signal d n which is required for adaptation process For adaptive filt r the tap weights will vary with time which are controlled by the adaptive algorithm The tap weights or the coefficient of the FIR filter will vary from sample to sample to minimize the mean square error 22 2 Infinite Impulse Response IIR Filter There are three structures commonly used to implement IIR filter which are direct form cascade form and parallel form The transfer function of an IIR filter can be expressed as
27. ent a software tools based on the concept The aim of this project is to create a software tools that should cover two adaptive algorithms which is Least Mean Square LMS and Recursive Least Square RES algorithm With this software the performance of both algorithm can be compared and the characteristic of both algorithms also can be determined The first stage to develop this project is through literature search where the implementation and theoretical of adaptive filter are studied From this literature search the concept of adaptive filtering is obtained thus enabling the project to go one more step further After understanding the concept implementation of theoretical studies is being implemented Designing the software using Visual Basic based on the theoretical concept and designing technique After completing programming this software testing have to be carried out For testing part the computation of adaptive filtering is tested based on the theoretical concept In this project LMS adaptive algorithm is succesfully being implemented in the software but RLS adaptive algorithm is not The LMS algorithm property and performance is being genearlised where it had been discussed in Chapter 4 From this project it shows that the step size and filter length of LMS algorithm plays an important role for performance measerement of LMS adaptive system The larger the step size and filter length the faster convergence time is obtained but this will
28. gurations are widely used So if one can come out with a software like that it will really mean a lot to the Digital Signal Processing DSP world This software can also be implemented into DSP processor ADSP 21065 L processor This processor comes with all software needed to develop sophisticated high performance DSP application 36 Appendix A Program Code of Adaptive Filter Implementation Option Explicit Dim w arr 1000 As Double Dim y arr 1000 As Double Dim x arr 1000 As Double Dim d arr 1000 As Double Dime arr 1000 As Double Dim f arr 1000 As Double Dim m As Double n As Double z As Double counter As Double Private Sub clear Click Text1 Text Text3 Text Listl clear List2 clear List3 clear Text4 Text form graph picture gph Cls End Sub Private Sub Command Click Dim check As Double Dim Dummy As Double Dim arr 1000 As Double new y 1000 As Double d arr 1000 As Double Dim x As Double t As Double Dime total 1000 As Double MSE 1000 As Double Dim As Double 13k fc sk sk sk se keoke sk kk kk 1 yn ERIE SEE I SE koe akokak sk k k Sk Pkk k k LMS Implementation check False z 0 e total z 0 form graph gph data 0 form graph list x clear form graph list y clear Do Until check True For n 0 To Textl Text 1 y arr n 0 d arr n 0 1 0 For m 0 To Text4 Text 1 Dummy n m If Not Dummy gt 0 And Dummy Val Text4 Text Then Do Until Dummy 7 0 And Dum
29. is software provides learning curves of the system where performance of the system can be analyse from this curves Figure 4 3 shows the Mean Square Error performance of the system while Figure 4 4 shows performance of the adaptation of initial tap weight to the optimum tap weight 24 DSP based Adaptive Filter The simulation results shown in Figure 4 3 shows that as filter length increased the MSE decay to constants state in faster manner So these clarify the statement made in Section 4 3 where as filter length increase the convergence rate become faster As can be observed from Figure 4 3 the MSE reach constant state approximately 10 iterations for system with filter length of 10 While for system with filter length of 2 the MSE reach constant state at approximately 70 iterations In real world these bring a huge effects to its computation complexity With lesser computation definitely the hardware to implement this system will be easier The graph parameter of Figure 4 3 y axes Mean Square Error MSE x axes No of iteration n V an mn a4 a4 034 2 0 r4 42 S UE d tiM M e sd ros HA ua a M ek We ue 4 UNE LT d n d 4 5 te e a ee ae ur DOE vi i ae ee recs oa rae at Ime quie i i i i i i i i i 2a24de L 2J2 2 Lb2224J22 2 Ll2 2242 22 L222J 2 WEN a 3 4 1 4 ieee cw cA WU Stu II M X 4o 7 ue c Mee id KT lo i Wo T m d um i20
30. l an adaptive system the MSE is small and the convergence time will become lesser but this will lead to more complex computational As larger filter length is used this mean that a much more complex computational is required and then much more complex hardware is required to model the system Thus in order to have a modelled a good system the step size and filter must be carefully chosen so that the stability and the computational complexity is taken into account 24 DSP based Adaptive Filter Chapter 5 Software Description This chapter will give a clear description of using this software As mentioned in Chapter 3 this software is programmed using Visual Basic language Thus it will create an atmosphere where user will easily get familiar within a short period The concept of using this software is easy to understand and user friendly This chapter gives user an opportunity to understand how to interface with the software in order to view the result of the simulation 5 1 Overview of Software Figure 5 1 illustrates the layout of the software As can be seen there are few parameters where user can set in im Form Of x File Open File igure 5 1 Adaptive based Software GUI 28 DSP based Adaptive Filter 5 1 2 Flow of Software Start End of program Assign signals parameter in Display output txt files in graph Load
31. lgorithm This experiment proved that as the filter length parameter is increased the rate of convergence of the LMS algorithm is correspondingly increased A reduction in the filter length parameter also has the effect of reducing the variation in the experimentally computed learning curve 4 3 Summary In this chapter the properties of Least Mean Square LMS algorithm has been discussed Each LMS properties have different affects to the performance of the system Normally in order to investigate the performance of the system using LMS algorithm learning curves is used Learning curves can be used to view the performance of LMS algorithm for both Mean Square Error MSE versus no of iteration and Tap weight versus no of iteration From experiment 1 and 2 it concluded that in order to successfully build an adaptive system the LMS algorithm parameter have to be taken into account The step size and the filter length of the algorithm play a huge role here This is because the step size and the filter length will determine how well does the system performs A large step size and within the range in equation 4 1 will give produce a system with small mean square error a shorter convergence time and provide better tobustness of a system The stability of the system will decrease as large step size is being implemented in the system Filter length on the other hand has the same affect to a model system When a large filter length is used to mode
32. lue True Then Optionl Enabled False Option2 Enabled False Option3 Enabled False End If End Sub Private Sub TAP Click Dim temp As String CommonDialogl Filter Text Files EXT TXT AII Files CommonDialog1 ShowOpen RichTextBoxl LoadFile CommonDialog1 FileName List1 Print LoadFile CommonDialogl FileName RichTextBoxl Text w arr counter Open CommonDialog FileName For Input As 1 Do Until EOF 1 Input 1 temp List1 AddItem temp Loop Close 1 End Sub 40 References 1 Simon Haykin Adaptive Filter Theory Prentice Hall Inc Englewood Cliffs NJ 1995 2 Emmanuel C Ifeachor and Barrie W Jervis Digital Signal Processing A Practical Approach Prentice Hall Inc Englewood Cliffs NJ 2001 3 John G Proakis Charles M Rader Fuyun Ling and Chrysostomos L Nikias Advanced Digital Signal Processing Macmillan Publishing Company New York 1992 4 C F N Cowan and P M Grant Adaptive Filters Prentice Hall Inc Englewood Cliffs NJ 1985 5 Widrow and Stearns Adaptive Signal Processing Prentice Hall Inc Englewood Cliffs NJ 1985 6 Leland B Jackson Digital Filters and Signal Processing Kluwer Academic 1986 7 S M Bozic Digital and Kalman Filtering Bozic 1994 8 Brian Siler and Jeff Spotts Special Edition Using Visual Basic 6 Que 1998 9 Samuel D Stearns and Don R Hush Digital Signal Analysis 58 edition Prenti
33. mpute Kalman gain vector k The Kalman gain vector can be obtained using s z n l x 14 x s z n 1 x 3 7 Stage 6 Update the autocorrelation matrix The autocorrelation matrix now is updated using z n s z n I k s z n 1 x 3 8 Stage 7 Update the tap weights The tap weight ofthe filter are updated w n 7 w n 1 ke n 3 9 18 DSP based Adaptive Filter Chapter 4 Property and Performance of LMS Algorithm 4 1 Properties of LMS Algorithm In this chapter the basic properties of LMS algorithm will be discussed These properties will then lead to the measurement of performance of LMS algorithm Here it will focus on LMS algorithm performance in respect to its convergence properties its stability and its minimum mean square error its robustness and how filter length affects its performance Then the simulation and results obtained from the software will be discussed in order to get a better idea how does the LMS properties affect the performance of LMS algorithm 4 1 1 Convergence Rate Convergence rate is the rates of determining the initial tap weight of the filter converges to the optimum tap weight The convergence rates of the LMS algorithm can be investigate by determining how the mean value of initial tap weight converges to the optimum tap weight In order to obtain convergence two requirements must be satisfied First the filter coefficients approach the optimum weight as n oo th
34. my lt Val Text4 Text If Dummy gt Val Text4 Text Then Dummy Dummy Val Text4 Text ElseIf Dummy 0 Then Dummy Dummy Text4 Text End If Loop End If y arr n Format List1 List n List2 List Dummy y arr n 0 Compute filter output Viti d arr n Format List3 List n List2 List Dummy d arr n 0 new y n y arr n Next e arr n Format d arr n y arr n 0 Compute error e total z Format e total z e arr n 2 0 MsgBox e total z Ife total z 0 Then check True If z Text2 Text Then check True Next MSE z Format e total z Text1 Text 0 add value to graph If Option3 Value True Then form graph list x Additem z form graph list y Additem MSE z form graph gph data form graph gph data 1 form graph label x Caption No of Iteration n form graph label title x Caption No of Iteration n End If modification to listl f arr z Text3 Text e total z Compute factor MsgBox f arr z For n 0 To Textl Text 1 t 0 For m 0 To Text4 Text 1 Dummy n m If Not Dummy gt 0 And Dummy lt Val Text4 Text Then Do Until Dummy gt 0 And Dummy lt Val Text4 Text If Dummy gt Val Text4 Text Then Dummy Dummy Val Text4 Text Elself Dummy lt 0 Then Dummy Dummy Text4 Text End If Loop End If List1 List n Listl List n f arr z List2 List Dummy t t 1 MsgBox Listl
35. nDialog1 FileName List1 Print LoadFile CommonDialogl FileName RichTextBoxl Text w arr counter Open Commonbdialogl1 FileName For Input As 1 Do Until EOF 1 Input Al temp List3 Additem temp Loop Close 1 End Sub Private Sub Example Click Dim counter As Double Textl Text 2 Text2 Text 200 Text3 Text 0 1 Text4 Text 4 Open App Path amp Tap weight amp txt For Input As 1 Do Until EOF 1 Input 1 vv arr counter Listl Additem vv arr counter counter counter 1 Loop Close 1 Open App Path amp Tap Inputs amp txt For Input As 2 Do Until EOF 2 Input 2 x_arr counter List2 Addltem x arr counter counter counter 1 Loop Close 2 Open App Path gt IDesired response amp txt For Input As 3 Do Until EOF 3 Input 3 d arr counter 39 List3 AddItem d arr counter counter counter 1 Loop Close 3 End Sub Private Sub Form Load form_graph Visible False form_graph list_x clear form_graph list_y clear End Sub Private Sub Inout_Click Dim temp As String CommonDialogl Filter Text Files TXT TXTJAII Files CommonDialog1 ShowOpen RichTextBoxl LoadFile CommonDialog1 FileName Listl Print LoadFile CommonDialogl FileName RichTextBoxl Text w arr counter Open CommonDialogl FileName For Input As 1 Do Until EOF 1 Input Al temp List2 AddItem temp Loop Close 1 End Sub Private Sub Option4 Click If Option4 Va
36. ncellation and prediction In real time LMS is easy to implement where the process of updating the filter tap weights coefficient are based on steepest descent algorithm 1 The coefficients are updated from sample to sample using the following equation w m 1 w n ue n x n 2 5 where w n is the tap weights ofthe digital filter e n 1s the error signal x n is the tap inputs u is the step size The resultant new weight based on equation 2 5 is only estimation but this will improve as the algorithm learns the characteristics of the signals The step size p is the parameter which control the stability and the rate of convergence 1 2 Thus a proper value of u must be assigned in order to ensure convergence The condition for convergence of the LMS algorithm in the mean square is 0 lt U lt 2 tap input power 2 6 where the tap input power is the sum of the mean square values of tap inputs u n u n l u n N 1 1 One draw back from LMS algorithm is that there is only one adjustable parameter which is u that affects convergence rate DSP based Adaptive Filter 2 3 2 Recursive Least Square RLS Adaptive Algorithm RLS adaptive algorithm uses least square method to estimate correlation directly from the input data This method allowed convergence rate to decrease and hence the computation for the process of obtaining optimum weight is faster compared to LMS algorithm The tap weights are updated using w
37. periment is 0 8 and Figure 4 2 shows that the LMS algorithm can successfully converge to 0 793 and become constant at iteration reached approximately 120 for step size of 0 5 Referring to Figure 4 2 all the tap weight doesn t converge to the optimum weight but it becomes constant at certain value which is very near to the optimum weight Hence this concludes that step size of 0 5 is the best step size to use with the LMS parameter in experiment 1 This is because the average mean square error becomes constant in the shortest period The robustness of the system is good since the difference between the optimum weight and the converged tap weight is the smallest Besides that the time taken for the LMS algorithm to reach optimum weight is also the shortest This experiment proved that as th step size parameter is increased the rate of convergence of the LMS algorithm is correspondingly increased A reduction in the step size parameter also has the effect of reducing the variation in the experimentally computed learning curve 4 2 2 Experiment 2 The second experiment is to observe how the filter length N affect the convergence rate So a set of parameter is used to perform this experiment Here the LMS algorithm parameter is set to be Step size u 0 1 Initial tap weight wo 0 No of iteration 200 Optimum weight 0 8 Using the above parameter and applied to the software the results of varying the filter length are obtained Th
38. project about It clearly state that the aims and objectives of the project It gives a brief idea how does the whole project is developed In chapter 2 the fundamental of digital signal processing where the structure of adaptive filtering is being discussed The theoretical of adaptive filtering explaining how does the conventional filter and adaptive algorithm being combined together to form adaptive filter Besides that this chapter also include various adaptive configurations and its application In chapter 3 it will discuss about the technique of designing the software using Visual Basic language An overview of Visual Basic and the reason of choosing this programming language are mentioned Then the implementation of LMS and RLS adaptive algorithm are being discussed In chapter 4 the properties of LMS adaptive algorithm are highlighted Analysis on the LMS algorithm s parameter is discussed in this chapter Besides that experiments carried out to performance analysis of LMS algorithm are also highlighted in this chapter In chapter 5 it will discuss about the software description It indicates how to interface with the software and give user a guideline to use it In chapter 6 it summarizes the whole project with the achievements obtained from the project research Future works for this project is also mentioned DSP based Adaptive Filter Chapter 2 Adaptive Filter Adaptive filters are digital filters capable of self
39. put signal x n Thus the output y n is the summation of the multiplication of each tap input with its respective tap weight The filter length N is the number of filters weight and k is the filter taps Figure 3 4 illustrates the process of convolution between the tap weight and the tap input E MANA ng e TS gt t Figure 3 4 The convolution y n of x n and wx n 16 DSP based Adaptive Filter Stage 4 Compute error Error is the difference between the desired input signals with the output signal of the adaptive filter It can be obtained using e n d n y n 3 4 Stage 5 Compute factor The step size u play an important role to determine the convergence rate of Least Mean Square method This stage is to compute factor of the set size withthe error obtained from previous stage This is for easier testing and upgrading purposes in the future Stage 6 Update coefficient This is the final stage of LMS computation model where the coefficient of the filter tap weights are updated using Wy n 1 wy n ue n x n k 3 5 Thus each tap weights of the respective tap inputs will be updated from sample to sample in order to minimize the mean square error 32 2 Implementation of Recursive Least Square Algorithm The major advantages of LMS algorithm lays in its computational simplicity but this lead to slow convergence especially when the eigenvalues of the a
40. ram will start the computation of filter Stage 6 Display output in graph After the computation of filter is successfully done then the graph showing the performance of adaptive filter will be displayed 5 2 User s Manual In this section the method to interface with the software is being interfaced by the user All the process being discussed in Section 5 1 2 will be implement in this section User will then have a brief description of using the software then 5 2 1 Load Example In order to load an example user can press Alt F then follow by clicking Load Example as shown in Figure 5 3 a This action will then fill in the entire blank boxes in the software shown in Figure 5 3 b The signal parameter which is loaded as an example in this program is first being set in text files Then from text files it is being transfer to the corresponding text boxes and list boxes 30 DSP based Adaptive Filter si Formi File Open File Load Example Clear a File is selected i Formi File Open File b Example is loaded Figure 5 3 Software GUI when certain events are clicked a File b Load Example 5 2 2 Assigning Signal Parameter This process can be done by pressing Alt O Then user can import their data which must be in text files TXT form For instance if user would like to apply value for tap weight then he has to click on Tap weight Then Dialog box shown in Figure 5 4
41. re 2 5 this configuration has same input applied to adaptive filter and unknown system The error signal s n is the difference between the output of the adaptive filter y n and the output of the unknown system din Thus if the adaptive filter successfully minimizing the error to zero the transfer function of the unknown system must be identical to the transfer function of adaptive filter The weight will then remain stable and unchanged as long as the transfer function of the unknown system does not change and then it can be said that the system is identified 2 4 2 Adaptive Inverse System Configuration The applications of adaptive Inverse System Configuration are Channel Equalization and Adaptive Equalization The structure of this configuration is shown in Figure 2 6 Y d n s n Unknown x n Adaptive y n Co e n System Filter L Figure 2 6 Adaptive Inverse System Configurations Input s n is applied to the unknown system and then to the adaptive filter where it then generate an output y n Input also applied to a delayed element to obtain a desired signal d n The delay element is used to ensure that the problem is casual and is solvable in real time system Similar to the Identification System Configuration the transfer function of the adaptive filter must be same with the transfer function of the inverse unknown system 2 4 3 Adaptive Noise Cancellation Configura
42. re 4 1 shows the Mean adaptation of initial tap weight to the optimum tap weight y axes Mean Square Error MSE The graph parameter of Figure 4 1 x axes No of iteration n Optimum weight 0 8 Figure 4 1 MSE performance using step size of a 0 5 b 0 1 and c 0 05 22 No of iteration 120 185 200 0 7930 0 7763 Tap weight 0 7538 23 c FES T 1 T T 1 T T 1 1 D i i i D i i i D i D i 2 D 1 D i D D ie ist Jala gi deii gui mini l nie ga am e l D 1 D 1 1 1 i D 1 i D 1 D 1 i 2 i D D 1 1 D te ee ee et ee ee ee ee cde 1 D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y e i 1 1 i 1 1 D 1 VS Te paa at de paa ate 1 i i D 1 1 D 1 1 D i D 1 i D o D 1 i D 1 1 a Vd ttt e E E doce be cc E le D 1 1 i 1 1 D i i D i 8 D i D 1 i pod epe Poser ege ep sess Te Ser ee qp ems i D i i i i D D i D i i um i D i i kd prd u 1 1 1 D 1 1 1 1 D D 1 D o D 1 D 1 D 1 D po SSN ho Pee So ges pec Sa es eeu i D 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 b e 1 1 1 1 1 1 D 1 1 Pr Mr Ad i 1 b 1 1 1 i 1 1 D i D D 1 i D 1 i D 1 i D i o D i D 1 D D i im SI Ic gt T ci 6B ry DI T IB BIT o ost 4D Oo CY KS MD O m 16 mB wh amp HO M AN d Im ko
43. that attempts to model the relationship between two signals in real time in an interactive manner Adaptive filters are well accepted in communication systems for echo cancellation and line equalization An adaptive filter is also suitable for real time control systems for different kinds of applications related to real time optimisation Adaptive signal processing is also expanding in other fields such as radar sonar seismology and biomedical electronics An adaptive filter could be implemented as an open loop filter or a closed loop filter The algorithm operates in an iterative manner and updates the adjustable parameters with the arrival of new data and current signal performance feedback parameters During each iteration the system will learn more about the characteristics of the input signal The processor makes adjustments for the current set of parameters based on the latest system performance i e the error signal e n The optimum set of values of the adjustable parameters is then approached sequentially Adaptive filters are often realized as a set of program instruetions running on a digital signal processor DSP based Adaptive Filter Generally four aspects can define an adaptive filter First the signals are being processed by the filter x n Secondly the structure that defines how the filter output is computed from its input signal Thirdly the filter parameters can be interactively changed to alter the filter s in out rela
44. tion Another configuration of adaptive filter is the adaptive noise cancellation configuration This configuration can be applied as noise canceling beam forming and ECG noise control Figure 2 7 shows the structure of the adaptive noise cancellation configuration s n n n vs Adaptive n n x n Filter yi Pen Figure 2 7 Adaptive Noise Cancellation Configurations d n 10 DSP based Adaptive Filter A correlated noise reference signal n n is applied to the adaptive filter and th output y n is compared with the desired signal d n Here the desired signal consists of a signal s n corrupted with a noise signal n n Hence whenever the adaptation takes place it will vary the filter weight which completely models the noise signal Thus it can be expected that the error signal is equal to the input signal e n s n when the filter s weights stop varying 2 4 4 Adaptive Linear Prediction Configuration Finally the last configuration is the adaptive linear prediction This configuration is applied to linear prediction coding signal detection adaptive CDM A receiver etc The structure of this configuration is shown in Figure 2 8 d n Adaptive x n gt z OV Fiter quU qo Figure 2 8 Adaptive Linear Prediction Configurations For this type of configuration when the error signal is adapted to zero then the adaptive filter will
45. tion Finally the adaptive algorithm that describes how parameters are adjusted from one time instant to the next 1 2 Project Aims and Objectives The main purpose of doing this project is to understand the concept of adaptive filtering With this concept a software tool named DSP based Adaptive Filter Software is created in order to perform comparison of using different parameter of Least Mean Square LMS and Recursive Least Square RLS adaptive algorithms The aims and objective of this project are e To introduce a software tool or a software learning kit which can help user to understand more about adaptive filtering e To generate a software tool to perform comparison of using different adaptive algorithms for different configuration so that engineer will have clear description which algorithm to use in order to get the best design e To enable the engineer or designer to choose the best parameter of adaptive algorithm in order to enhance performance of their design e To enhance engineer or designer to do further investigation and research on adaptive filter based system by providing this software tool e To increase more system using application of adaptive filter since this software tool can help boost the performance of the systems e To minimize the time and cost of providing adaptive filter based system configurations e To boost self development in developing extra knowledge of other field for instance softwar
46. tion Label is used to display information to the user text boxes is used to gather information and command button is used to respond to user actions Procedures are small routines that callable from anywhere in application These routines will perform the routines function whenever it is called 12 DSP based Adaptive Filter s Projccti Microsoft Visual Basic design File Edit View Project Format Debug Run Query Diagram Tools Add Ins Window Help B amp Ti real oc pn arrat 3m Pej i S Projecti Formi Form H Projecti Project B Forms E Formi Formi Forms windows which used to build user interface 20 09 lap 1 3D False Gi exso000c le 2 Sizable Controls interface tools where can be selected using click and drag technique Properties indicating the property of each element in the window 0 Solid 1 True Bl exo0000c Returnsjsets the text displayed in jan object s title bar or below an mee 4008 ES ASA ZA DAVSAR EERE uma E diagram doc Microsof BE intro2 doc Microsoft al FINAL YEAR PROJECT E introduction doc Mier s Projecti Microsoft AA Figure 3 1 Visual Basic s design environment Events is the most important concept of Visual Basic programming where it response to user interaction with the keyboard or mouse It can be said that events are messages to the application An event proc
47. ttings a Form for sttings b Form for color settings kl 25 26 28 29 31 32 33 33 34 List of Abbreviation DSP FIR IIR LMS RLS MSE VB GUI Digital Signal Processing Finite Impulse Response Infinite Impulse Response Least Mean Square Recursive Least Square Mean Square Error Visual Basic Graphical User Interface DSP based Adaptive Filter Chapter 1 Introduction Filtering is a very common task in Digital Signal Processing world Filtering means a process of extracting a data which was corrupted by noise In order to obtain the original noise free source the corrupted data must undergo a filter There are basically two ways of designing a filter where one is by knowing the exact information of the signal source property the conventional filter and the other one is the contradiction of the previous statement where no exact information ofthe signal source property is known When filters work in an unknown environment where identification is impossible it must be capable of adapting to such situation so that it can perform optimally Thus adaptive filter can be used to solve this problem Adaptive filters are capable of obtaining the necessary information without knowing any priori information of the relevant signal characteristics thus enabling the filter to react even there is any changes to the environment 1 1 General Description of Adaptive Filters An adaptive filter is a computational device
48. ue n x n k Figure 3 2 Flowchart for the LMS adaptive filter 14 DSP based Adaptive Filter The stages to implement LMS adaptive filter are Stage 1 Initialize w n and x n k This stage the filter s weight wx n and the input data after each delay x n k is initialized Thus for instance the input signal is x n 10 4 3 2 1 4 for t 10 52 3 coss 3 1 Then the input signal after one delay will be shifted to the right by one space where it become x n 1 0 0 4 3 2 1 4 for t 10 1 2 3 2 3 2 Figure 3 3 illustrates equation 3 1 and 3 2 in discrete input signal form for better understanding Original data Data after undergo one delay xn x n 1 A t 0 1 2 A t 0 1 2 u mu u Input data shifted to the right after one delay Figure 3 3 a Discrete signal of input data b Discrete signal of input signal after one delay Here each weight w n where n 0 1 N 1 is set to zero Filter length N 15 DSP based Adaptive Filter Stage 2 Read d n and x n Desired reference signal d n and the input signal x n Stage 3 Filter x n In this stage the adaptive filter output is obtained using this equation N I yin gt wi n x n k 3 3 k 0 Equation 3 3 shows that the adaptive filter output is basically the convolution of tap weight vv n and in
49. utocorrelation matrix have a large spread Hence in order to have faster convergence thus RLS algorithm is used The computational procedure for Recursive Least Square RLS algorithm is more complex compared to the LMS algorithm It uses least square method where it deal directly with the data sequence x n and obtain estimates of correlations from the data Now lets have a look of how RLS algorithm computation procedure to obtain new filter coefficient is done The important parameters of RLS algorithms N is the number of filter weights s 1 forgetting factor k is the Kalman gain N by 1 vector x x n x n 1 x n N 1 is the input samples and w wo W7 ww i is the filter weights where each weight is set to 0 Stage 1 Initialize w n k and x n The filter s tap weight and the tap inputs to the respective tap weights are obtained Stage 2 Read d n and x n Desired reference signal d n and the input signal x n are obtained 17 DSP based Adaptive Filter Stage 3 Filter x n In this stage the adaptive filter output is obtained using this equation N 1 ymn 2 we n k x n 3 5 k 0 It can be observed that the output of the adaptive filter at time n based on use of the filter coefficients at time n Stage 4 Compute error Error is the difference between the desired input signals with the output signal of the adaptive filter It can be obtained using e n d n y n 3 6 Stage 5 Co
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